In both TvN dramas is ML well known idol and female lead is obsessed and stalking ML
Both are romantic comedies

Both main protagonists suffering from cancer can make contract with "devil" to get extra time to life. In If Cats Disappeared From the World can postman erase one thing from the world and then get extra day to life. In Doom at Your Service Tak Dong Kyung makes a contract with Myeol Mang for a hundred days to live how she wants, risking her everything.

both are really crazy makjangs with crazy plot, adults, rich people and stuff happening around them

Mature protagonists (adults)
Infidelity of partners
Parents behaviour affects their childrens
Greed for connections to social elite, power and money

Both TvN dramas are based on the webtoon.
They're about girls that are not popular at school, both are comedies and have rich male leads. Both contains social problems, bullying, misunderstandings and betrayals.

Both have the concept of the frugal FL teaching her way of life to the ML after the ML lands in trouble for his way of spending money

They both deal about possession and evil spirits and the fight against them. They both have the exact same feeling.

both dramas revolve around a rich boy and poor girl scenario set in high school and are light fluffy dramas

Modern day Chinese drama about female fashion designers. Both dramas has bussines, romance and rich male lead.

Modern day Chinese drama about female fashion designers. Both dramas has bussines, romance and rich male lead.

The only similar thing is that both korean dramas show relations between South and North Korea.
Otherwise the plot is completely different cause CLonY is romantic story about woman from SK and male soldier from NK.
Search is thriller, mystery, horror drama about virus.
But I believe that you'll love both since they're both unique dramas with interesting plot. Plus you can watch CLonY after Search if you need something similar but a little bit lighter and cutter (I guess?)

Both these dramas are gripping thriller that will keep you on edge.
Makjang, murder, mystery, friendships, a lot of drama and bitterness are to be expected.